Sadly I don't. I think it came in a box covered in the same pattern as the backing. For some reason I keep thinking it's connected to cigarettes? I don't smoke so I don't know if those companies come out with cards you can purchase from a catalog or something.
It's unlikely that this was made as an advertising deck for a cigarette company. First of all, the company name/logo would appear somewhere - and frequently! Second, the cost of printing the cards on plastic would make them prohibitively expensive to simply give away as a premium. Custom deck designs like this rarely get printed on plastic today, and it would have been an order of magnitude more rare back when you first acquired this deck.
Would you perhaps know the country of origin? That would help as well. Some countries have very few card manufacturers in the first place, so you'd at least be able to narrow down the list of possible makers quickly. Even in a country as large as the US, most of the card manufacturing that takes place here comes from just one company, the United States Playing Card Company (USPC). I'm told there are few manufacturers in the UK and Australia as well, usually with a single company dominating the marketplace.
I got this deck in 9th grade off some kid for $5.00 He said he could always get more so I assumed that they were that expensive to make lol No idea of the country of origin.
I just looked at a set of Molla Cards which look very similar in texture but those are made out of pvc and now I'm wondered if these are too. I just assumed plastic. Not sure if that would narrow down a list of companies.